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Register a new userStatistics of optimal information flow in ensembles of regulatory motifs
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Genetic regulatory circuits universally cope with different sources of noise that limit their ability to coordinate input and output signals. In many cases, optimal regulatory performance can be thought to correspond to configurations of variables and parameters that maximize the mutual information between inputs and outputs. Such optima have been well characterized in several biologically relevant cases over the past decade. Here we use methods of statistical field theory to calculate the statistics of the maximal mutual information (the `capacity) achievable by tuning the input variable only in an ensemble of regulatory motifs, such that a single controller regulates N targets. Assuming (i) sufficiently large N, (ii) quenched random kinetic parameters, and (iii) small noise affecting the input-output channels, we can accurately reproduce numerical simulations both for the mean capacity and for the whole distribution. Our results provide insight into the inherent variability in effectiveness occurring in regulatory systems with heterogeneous kinetic parameters.
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Based on a recently proposed non-equilibrium mechanism for spatial pattern formation [cond-mat/0312366] we study how morphogenesis can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problem of domain formation and proportion regulation in the presence of noise and cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. A further focus of this paper is a detailed study of noise-induced dynamics, which is a major ingredient of the control dynamics in the developmental network model. A master equation for domain boundary readjustments is formulated and solved for the continuum limit. Evidence for a first order phase transition in equilibrium domain size at vanishing noise is given by finite size scaling. A second order phase transition at increased cell flow is studied in a mean field approximation. Finally, we discuss potential applications.
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multi-cellular organisms.
Gene transcription is a stochastic process mostly occurring in bursts. Regulation of transcription arises from the interaction of transcription factors (TFs) with the promoter of the gene. The TFs, such as activators and repressors can interact with the promoter in a competitive or non-competitive way. Some experimental observations suggest that the mean expression and noise strength can be regulated at the transcription level. A Few theories are developed based on these experimental observations. Here we re-establish that experimental results with the help of our exact analytical calculations for a stochastic model with non-competitive transcriptional regulatory architecture and find out some properties of Noise strength (like sub-Poissonian fano factor) and mean expression as we found in a two state model earlier. Along with those aforesaid properties we also observe some anomalous characteristics in noise strength of mRNA and in variance of protein at lower activator concentrations.
We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a Boltzmann-like distribution ($propto e^{F/T}$) where $F$ is a linear combination of fluxes and the `temperature parameter $Tgeq 0$ allows for fluctuations. The zero-temperature limit corresponds to a Flux Balance Analysis scenario, where an objective function ($F$) is maximized. As a test, we have inverse modeled, by means of Boltzmann learning, the catabolic core of Escherichia coli in glucose-limited aerobic stationary growth conditions. Empirical means are best reproduced when $F$ is a simple combination of biomass production and glucose uptake and the temperature is finite, implying the presence of fluctuations. The scheme presented here has the potential to deliver new quantitative insight on cellular metabolism. Our implementation is however computationally intensive, and highlights the major role that effective algorithms to sample the high-dimensional solution space of metabolic networks can play in this field.
Microbial metabolic networks perform the basic function of harvesting energy from nutrients to generate the work and free energy required for survival, growth and replication. The robust physiological outcomes they generate across vastly different organisms in spite of major environmental and genetic differences represent an especially remarkable trait. Most notably, it suggests that metabolic activity in bacteria may follow universal principles, the search for which is a long-standing issue. Most theoretical approaches to modeling metabolism assume that cells optimize specific evolutionarily-motivated objective functions (like their growth rate) under general physico-chemical or regulatory constraints. While conceptually and practically useful in many situations, the idea that certain objectives are optimized is hard to validate in data. Moreover, it is not clear how optimality can be reconciled with the degree of single-cell variability observed within microbial populations. To shed light on these issues, we propose here an inverse modeling framework that connects fitness to variability through the Maximum-Entropy guided inference of metabolic flux distributions from data. While no clear optimization emerges, we find that, as the medium gets richer, Escherichia coli populations slowly approach the theoretically optimal performance defined by minimal reduction of phenotypic variability at given mean growth rate. Inferred flux distributions provide multiple biological insights, including on metabolic reactions that are experimentally inaccessible. These results suggest that bacterial metabolism is crucially shaped by a population-level trade-off between fitness and cell-to-cell heterogeneity.
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